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I know this might not matter much especially if you're on ChromeOS or MacOS, but outside of the blur effect in the background, I made my profile picture entirely in Microsoft's default Paint app. Literally just took the pencil tool, maximized line thickness, and then started going.
.........i typed this whole post up but only some of it is applicable to phone users. im posting it anyway
if possible you might want not a website but an offline program. i used a paid program (paint tool sai), but some free software i know of for desktop include firealpaca and krita. honestly, as dz said, if you learn it well enough, you can make nice art in ms paint. it depends on what you're looking to do. i don't know much about phone/tablet programs but if someone else wants to add to this feel free
if you're looking for a collaborative canvas, magma (formerly known as aggie.io) is a big one
i remember a while back somebody posted about a very simple online drawing canvas & art sharing site on the profile post wall. no memory of who or what the site was. i wanted to check it out, too. sad
none of these are splatoon-specific but (loading screen tip!) you can draw inklings in whatever program you want